What is with these questions lately? I know this is the "newbies" section, but really...
edit a few hours later -- I got called as soon as I started my reply: at least this particular question has some validity because tagging a person requires the tag be made with the ball (or the hand/glove holding the ball), so I don't mean the previous statement as "harsh" as it probably seems.
I agree. And, I think the poster does not understand the importance of the positioning of (in this instance) F3.
With R1, R3, F3 was likely holding R1 on. So, on the pitch, F3 likely moved a step or two fair, and maybe tried to field the ball. If so, the ball might have gone "through or immediately by" F3, so R1 would NOT be out.
Or, maybe this was LL and F3 was playing back. In that case, R1 IS out.
But, if R1 is out, the ball is dead. Conversely, if the ball was allowed to stay live, then R1 should not have been out. You can NEVER have the situation suggested by the OP where the runner is out for being hit by the batted ball, but the ball remains live.
A couple of points here: 1) Under OBR, "passed" means "through or immediately by" the fielder, not merely "beyond" the fielder, and the runner must be immediately behind the fielder.. Basically, if the runner could reasonably have expected the fielder to field the ball, the runner is protected if he doesn't have time to move. BUt, if, for example, there's a biog shift on, and the runner is hiton the other side of the infield, the runner is still out. 2) "Step and a reach" referes to interfering with the fielder, not to interfering with the ball. The runner is always protected from (non intentional) interference on a deflected ball, no matter how far waya it is or who did the deflecting (it applies to the pitcher as well).
I'd say you're wrong for FED (see below), but now right for OBR (and your first answer for OBR was wrong).
For NCAA, the wording in Rule 7-6 (Batting; Fair Ball) is different from what you have above (from Rule 2 - Definitions). The wording in Rule 7-6 DOES NOT include "equipment." I think it's the same as OBR.
d. While on or over fair ground, touches an umpire or player; or
FED: 2.16.1 SITUATION D: B1's bunt rolls up the first-base line where it hits B1's bat that was lying on the ground in fair territory. The ball deflects into foul territory. Is the ball fair or foul? RULING: The ball is foul, provided the bat was not placed there intentionally. The bat is considered to be part of the playing field. (2-5-1, 2-8-1, 8-4-1d)